(134a) Inferring Equilibrium Protein Binding Using Fret Imaging Data

Fluorescence Resonance Energy Transfer (FRET) is fast emerging as a powerful technique to visualize molecular interactions inside living cells. Quantitative FRET imaging promises to measure the spatial distribution of protein concentrations and their interactions inside live cells expressing specifically labeled proteins (Hoppe, et al., Biophys. J, 83:3652, 2002). Recent advances in microscopic techniques, hardware, and 3D-reconstruction algorithms allow for good spatiotemporal resolution and 3D detection of protein interactions by FRET (Hoppe et al., SPIE, 6089 2006). These 3D-FRET experiments give rise to complex data sets with large numbers of images of a single cell, highlighting the need for data analysis and abstraction. In particular, determination of an in vivo equilibrium dissociation constant K_d will greatly aid the evaluation of protein-protein interactions and the reconstruction of cellular signaling networks.

We have developed an algorithm to estimate K_d from FRET image data. Estimation of K_d from these images is complicated by the lack of understanding of contribution of the imaging process and propagation of noise, the presence and participation of unlabeled proteins in the interaction and possible variation of K_d between subcellular regions or protein states. Our algorithm takes deconvolved FRET images and uses the intensity/concentration values of individual 3D image volume elements (voxels) to calculate a probability distribution for K_d. Here, we consider the bimolecular interaction of labeled proteins both in the absence and presence of endogenous (unlabeled) proteins. In the latter case, we must account for the competition among the labeled and unlabeled species, and hence to solve the related balance equations for each voxel.

We first show the performance of our algorithm in recovering the known equilibrium dissociation constant for a hypothetical 3D test dataset. We then show the influence of various image-specific, cell-specific, and experimental parameters on the accuracy of K_d inference from our algorithm. In particular, microscopic imaging results in the convolution of the true 3D distribution of fluorescently-tagged molecules with the instrument's point spread function as well as the addition of detection noise, and the influence of these on the calculations are investigated. We also study the effect of voxel size on K_d inference. For example, analysis of image data with larger voxels (low resolution) provides less spatial information, but the results are more robust due to improved signal to noise. These calculations also cannot identify the possibility of multiple disassociation constants. On the other hand, analysis of image data using smaller voxels (high resolution) is more susceptible to variance arising due to concentration variability. We show that our method can be used to help identify optimal voxel size to be used for calculation. We test the performance of algorithm for robustness with respect to experimental and cell-specific variability. Next, we show that using the proposed method one can also identify multiple binding affinity states of proteins, and also estimate the relative abundance of a given binding state. These results, along with the original images, can be used to identify regions of active protein function within the cells. Further, we show the results of our algorithm for a more general case wherein not all the proteins of a type are labeled, i.e when endogenous protein levels are significant. Finally, we show the performance of our algorithm on real 3D-FRET data set in which we examine the binding of yellow and cyan fluorescent protein-tagged signaling proteins (Rac and PBD) in living cells. We also discuss possible extensions of the algorithm that will allow us to infer kinetic information from 4D (x,y,z,t) FRET data.